Possible problem when two clients update the same record?

Hi all.

I'm converting a dos based application using DBase files to PostgresSQL.
The application is a pawn shop system.

The dos application works as follows:
Table A holds all items which the customers bring to the shop.
Table B has one record for each day which holds the totals (pieces,
costs, etc.) for this particular day.
When B is updated, the particular record gets locked, updated and released.

The new application works this way:
- start a new transaction,
- insert the new record in A,
- the insert operation fires a trigger which updates B
- the transaction is committed.

Now my question:
What happens if two clients insert a new record to A at the same time?
Will B get updated correctly or will one value get lost?

I'm using PostgresSQL 8.0.2 under Windows, the client is written
with Delphi 7 + ZEOS.

Thanks in advance.

Karsten